For the first time, a newly developed Lattice Monte Carlo (LMC) method is used to determine concentration profiles for combined mass diffusion and chemical reaction. Different chemical reaction models are considered: instantaneous reaction, irreversible reaction and reversible reaction. Several simple problems are addressed so that LMC solutions can be compared to exact analytical and numerical reference solutions. Excellent agreement between analytical solutions and numerical results is obtained. In addition, a more complex scenario is considered in order to present the capability of the new method.